Tuesday, 8 December 2015

This afternoon, I lectured to my 2nd year students on Lewis and Stalnaker on possible worlds (with a bit of Kripke thrown in since we'd done the 1st lecture of Naming and Necessity two weeks ago). I included these two papers in the syllabus for the same reason I did last year -- because they are pieces of work of historical importance for their role in the debate on realism w.r.t. possible worlds. And like last year, I found both pieces difficult to lecture on, not because they are especially difficult, or especially problematic, but because, as a modal logician, I simply don't care. Resolving this debate -- whether possible worlds really are "out there" like Lewis thinks or whether they're more of a pragmatic tool as Stalnaker thinks -- will not change my practice one whit.

I try not to let my students know that I feel this way (I try to keep my philosophical "politics" out of the classroom -- except when the opportunity to rant on why I think "not philosophical enough" is a horrible criticism, but that is not apropos here), but I do try to let them know that there is more to the issue than resolving the debate, there is the question of whether the debate needs to be resolved before modal logicians can go about their business with impunity. Last year I put it as an essay question, but I don't remember if anyone took it up. This year, in yesterday's tutorial I divided the group into two and randomly told one "You prepare a case in favor of realism", and the other group "You guys get anti-realism", and during the ensuing discussion, I heard someone sort of whisper to someone else "Does it matter?", which I thought an appropriate to revisit the issue. We discussed it some in the tutorial, with one person feeling quite strongly that if one didn't properly settle the 'foundational' issues, then there would be no guarantee that the modal logician wouldn't one day be led astray. At the end of lecture today I posted two questions hoping to get people's gut feelings -- who thinks Lewis is right, who thinks he's not, and who thinks the question has to be resolved, and who thinks it doesn't. As expected, I got roughly equal hands for each, and was lucky enough to have two people willing to articulate their gut feelings. One (on the side of "yes, we do") argued from the basis of metaphysical possibility: If we're going to use possible worlds for analysing metaphysical possibility, we're sure going to want to know if they are metaphysically possible! The other said that you might need to look at reality to determine which axioms you adopted, but after that, it shouldn't matter what possible worlds in fact are when you start using them as a tool in modal reasoning.

All of this set me up to spend some more time thinking this afternoon about why I don't care. It's a rather scientific, rather than philosophical, position to take -- scientists don't care what the "real nature" of particles are (well, except for the foundationalists, i.e., the physicists), mathematicians don't care what numbers "really" are, modal logicians don't care what possible worlds "really" are, etc. The foundational issue raised in the tutorial yesterday gave rise to an apt comparison with mathematics: Mathematicians don't really care about what numbers are, because whatever they are, they sure work really really well, and by now it seems highly unlikely that we could discover something about what numbers are that would cast the results that we've derived using them into doubt. Modal logic isn't in quite the same position with respect to possible worlds, but it seems similar.

I also thought about what a situation in which it mattered what possible worlds were, metaphysically, would look like -- in what sort of situation would the metaphysical nature of possible worlds make a difference? Well, when discussing metaphysical possibility/necessity, as noted above. I happen to find that concept a highly dubious one (on extra-logical grounds), so I'm happy to simply put up my hands and say "that is not a modal concept I am interested in explicating". But as I tried to come up with concrete scenarios in which modal logic is applied, rather than simply theorized about, in each of these cases, the notion of possible world was interpreted as something quite concrete: For example, states of a computer programme. Then I thought about the other student's comment about needing to hash out what the right axioms were, and that possibly being when it was necessary to know something about the metaphysical status of possible worlds. But what is it that axioms specify? Do they specify anything about the worlds themselves? No: What modal axioms do is specify how the worlds are related to each other, and these axioms will hold (or not) in virtue of the relations between the worlds -- whatever the worlds may be. They may be Lewisian possible worlds, they may be states of a computer, they may be moments in time, they may be pebbles, they may be fruitcakes. The axioms -- that which really is the meat of modal reasoning -- are all about how the worlds are related to each other, and not about how the worlds are composed [1].

And that is at least part of the reason why I, as a modal logician, don't really care about what possible worlds are.

[1] At this point, I realize that everything that I've been saying is about propositional modal logic, and that if what you're interested in is quantified modal logic, then you might object that how the worlds are composed, i.e., what objects are in them and what properties those objects have, is of crucial importance, AND that the axioms adopted will have consequences for the internal composition, e.g., whether the Barcan or Converse Barcan formulas are axioms. To which I would reply: Hmmm, this is very interesting, I will have to think on the case of quantified modal logic further.